Superparamagnetic Clustering of Data

We present a new approach for clustering, based on the physical properties of an inhomogeneous ferromagnetic model. We do not assume any structure of the underlying distribution of the data. A Potts spin is assigned to each data point and short range interactions between neighboring points are introduced. Spin-spin correlations, measured ( by Monte Carlo procedure) in a superparamagnetic regime in which aligned domains appear, serve to partition the data points into clusters. Our method outperforms other algorithms for toy problems as well as for real data. [S0031-9007(96)00104-4] Many natural phenomena can be viewed as optimization processes, and the drive to understand and analyze them yielded powerful mathematical methods. Thus when wishing to solve a hard optimization problem, it may be advantageous to identify a related physical problem, for